Re: Still Negative Maternal Variance

# Re: Still Negative Maternal Variance

```Dear Hugo,

Negative variance estimates are not uncommon.
COnsider a simple balanced sire model for which
an appropriate analysis of variance is
Source  df       MS       E[MS]
SIRES  s-1    SireMS    Ve + kVs
ERROR  n-s    ErrorMS   Ve

In this ANOVA, the SIRE and ERROR Mean squares are independent.
If Vs is small, it is quite likely that SireMS will be smaller than
ErrorMS.  If you estimate Vs by equating meansquares to their expectation,
[SireMS - ErrorMS]/k will be negative and this is what unconstrained REML
will give for the Sire variance component.

Constrained REML would estimate Ve as [(n-s)*ErrorMS + (s-1)*SireMS]/(n-1)
and Vs as 0.

In your example, it appears there is no maternal variance.
I suggest you proceed to drop mat and pe from the model. I expect
a negligible decrease in LogL indicating there is no meaningful
maternal variance [either genetic or environmental]

It is possible that the maternal genetic component would increase if
pe is dropped from the model but I do not think it will increase enough to
become positive

Best wishes

Arthur

>
>
> Hello:
>
> With this .as file
>
> Birth weight
>  ani    !P
>  mat    !P
>  pe     6803
>  sex    2 !A
>  aod
>  aod2
>  sy     50 !A
>  AmS
>  Dd
>  Dm
>  bw
> PE2_2.prn !MAKE
> BW21.prn
> 0 0 1
> ani 2
> 2 0 US 1.16 .0 .287
> ani
>
> I got this estimates for variances and covariances:
>
>  Source       Model  terms     Gamma     Component    Compnt/StndErr
>   pe             6803   1572  0.781423E-03  0.805809E-02      0.02
>   Variance       3132   3099   1.00000       10.3121         19.76
>   ani         US=UnStr     1  0.311831       3.21562          5.15
>   ani         US=UnStr     1  0.188442E-01  0.194323          0.64
>   ani         US=UnStr     2 -0.207402E-02 -0.213874E-01     -0.06
>
> I have two questions:
>
> 1) It is possible to obtain negative variance estimates with the REML
> algorithm
> used in ASREML? (i.e., this is something that you can expect in some
> situations?)
>
> 2) There is something wrong in my model setting that may explain the
> negative estimate?
>
> Thank you again
>
> Hugo
> ================================
> Hugo Montaldo
> Research Fellow
> Division of Animal Science
> University of New England
> Armidale, NSW 2351
> Australia
>
> Phone  61 2 67 733004
> Fax    61 2 67 733275
>
> E-mail hmontald@metz.une.edu.au
> http://metz.une.edu.au/~hmontald/
> ==================================
> "Volver a los diecisiete despues
> de vivir un siglo
> es como descifrar signos sin ser
> sabio competente"
>        -Violeta Parra

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
Arthur Gilmour PhD                    email: Arthur.Gilmour@agric.nsw.gov.au
Senior Research Scientist (Biometrics)                 fax: <61> 2 6391 3899
NSW Agriculture                                             <61> 2 6391 3922
Orange Agricultural Institute               telephone work: <61> 2 6391 3815
Forest Rd, ORANGE, 2800, AUSTRALIA                    home: <61> 2 6362 0046

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